উঞ५ॺঞ५ॺ॥থॡজ‫৾ੵॺش‬ভ‫ؙ‬ਸ਼їћ৚३থএ४क़঒૛ધૐ‫ق‬їѕіќফіѕা‫ك‬

ULTIMATE DEFORMATION CAPACITY OF UNBONDED POST-TENSIONINGMONOSTRAND ANCHORAGES UNDER MONOTONIC AND HIGH-AMPLITUDECYCLIC LOADINGLuis A. BEDRIÑANA
Kaiwei ZHANG
Katsuhito OSHIMA
Minehiro NISHIYAMADoctor candidate, Kyoto University
Graduate student, Kyoto University
Senior Engineer, Sumitomo (SEI) Steel Wire Corp.
Professor, Kyoto University

Abstract: This paper presents the principal results of an experimental investigation on the ultimate
behavior of monostrand post-tensioning anchorages subjected to high-amplitude cyclic loads. In addition,
this paper addresses the influence of anchorage type, loading pattern and strand size on the ultimate
capacity of the anchorages. Specimens consisted of monostrands assembled with anchorages at both ends.
Two types of commercially available anchorages were tested. The results showed that ultimate
displacement capacity of the strands were limited by fracture of some wires inside the anchorages, withstrains as low as 1.42%.
Keywords: anchorage, unbonded, post-tensioning, monostrand, cyclic loading, self-centering.
1. INTRODUCTION
During the last decades, there has been an increasing interest in applying unbonded post-tensioned (PT)precast concrete (PCa) structures in seismic regions to control residual damage [1]. Unbonded PT anchorage
systems have been largely used in PCa members subjected to service load, but their application as earthquakeresistant members is not well documented. Moreover, it was noted that cyclic loading on unbonded PT strandanchorage systems might cause premature failure of strands inside anchorages [2,3]. Consequently, further
research is needed on unbonded PT anchorages for their seismic applications expected to meet performance-basedcriteria.
This paper describes the results of an experimental evaluation of the behavior and failure mechanism ofmonostrand anchorages subjected to cyclic loads. In addition, this paper addresses the influence of high-amplitude
low-frequency loading on the elongation capacity of strand-anchorage at fracture.
2. OVERVIEW OF THE EXPERIMENT
Test specimens consisted of monostrands assembled with anchorages at both ends. Table 1 describes theconfigurations used in the test. Seven-wire PT monostrands, with diameters of 12.7 and 15.2mm were considered.
The nominal fracture loads (Fpu) of the strands were 183 and 261kN for the 12.7 and 15.2-mm strands,respectively. The nominal cross-sectional areas were 98.7 and 138.7mm2 for the 12.7 and 15.2-mm strands,respectively. The measured breaking loads (Fpu,m), as reported in the mill sheet, were 197 and 278kN for the 12.7and 15.2-mm strands, respectively. Figure 1 shows details of the anchorages used in this test. Two types ofmonostrand anchorage were studied: single-use grip barrel anchor (BL) and casting plate anchor (CP). Generally,
CP anchors are made from grey ductile cast iron, whereas BL anchors are manufactured from high carbon steel.
The difference of materials on the two types of anchorage produces different hardness of the interior surface(where wedges are located), which may lead to different gripping conditions of the wedges. The sizes of theseanchorages corresponded to the size of strand used (Table 1). In addition, two-piece (referred to as 2P herein) andthree-piece (referred to as 3P herein) wedges were used. It is important to note that 2P wedges had vertical slits atthe top part (Fig. 1) and the 3P wedges were used with a binding ring at the top part, which helps in reducing
differential setting by holding the pieces together. All test samples were obtained from one manufacturer.
Figure 2 presents the general test setup, in which tensile loads were applied by a 300 kN-capacity servohydraulic computer-controlled material testing system. Steel plates were attached to the testing machine to enableinstallation of strands and anchorages. Vertical alignment of specimens was carefully checked during the entire
installation process and no initial preload was applied to the anchorages. The anchor to anchor length (Lps) was
about 1060 and 1065 mm for specimens with BL and CP anchorages, respectively. As for the measurement
systems, four strain gauges and three linear variable displacement transducers (LVDT) were used in each of thespecimens, as can be seen in Fig. 2. The central LVDT was fixed to the steel loading plates to capture total
elongations and the other two LVDT were attached at each anchorage zone to measure relative movement ofstrands into the anchorages. The strain gauges were attached along a single wire’s axis (i.e. with a slight angle

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1.2

D15-BL-2-M-4
(a)

1.0

0.80.6İİİ

0.40.2

fpu=1882 MPa

0.0
012

Normalized stress (fp/fpu)

1.2

34
Strain (%)

56

0.8

0.6
0.40.2İİİ

fpu=1854 MPa

0.0012

34
Strain (%)

5

D15-CP-3-M-1(c)

1.0
0.8
0.6
0.40.26İİİ

fpu=1882 MPa

0.00

1234
Strain (%)

1.2

D12-BL-2-M-1(b)1.0Normalized stress (fp/fpu)

1.2

Normalized stress (fp/fpu)

Normalized stress (fp/fpu)

neglected to eliminate inaccurate measurements. Then, the stress-strain curves were shifted along strain-axis so
the curves start at zero strain. Furthermore, the yield strength was calculated as the stress offset of 0.2% plasticstrain and the corresponding calculated elastic modulus.

56

D12-CP-2-M-2(d)

1.0
0.8
0.6

0.40.2İİİfpu=1854 MPa

0.001234
Strain (%)

56Fig. 4 Stress-strain curves under monotonic load
1.2a)D12-BL

Normalized stress (fp/fpu)

Normalized stress (fp/fpu)

1.2
1.0

0.8
0.6
cyclicmonotonic

0.40.2

fpu=1854 MPa

0.001234
Strain (%)

50.8

0.6
0.40.2

fu=1882 MPa

0.006b)

D12-CP

1.012

34
Strain (%)

cyclicmonotonic
56Fig. 5 Typical stress-strain curves under cyclic loading
3.1 Typical stress-strain curves
Figure 4 presents the different types of normalized stress-strain curves (fp/fpu-Hp curve) obtained from four
samples under monotonic loads. For each sample, it can be observed that the initial stiffnesses of the three types ofcurves were different, mainly because of the different information conveyed. As it was mentioned previously, H1
curve included the effect of anchorage seating and this influence was noticeable at the initial part of the curve
where some nonlinearity was observed in all samples; consequently, this curve is not representative of the ultimate
strain capacity of strand-anchorage systems. The influence of anchorage seating was then eliminated in the H2curve, which gives a better representation of engineering strand strains and the ultimate deformation capacity. On
the other hand, H3 curve was obtained directly from strain gauges, showing deformations of individual wire
(material behavior) rather than of the strand. Since the engineering stress and strain of strands are importantparameters for designing, the ultimate deformation capacity is reported from H2 curve hereinafter.
Figure 5 shows normalized stressȸstrain curves, corresponding to H2 definition, obtained from samples
subjected to cyclic loading. In this figure, a monotonic stress-strain curve of one sample is also plotted forcomparison. As it can be seen, the specimens were subjected to inelastic cyclic deformation, which extended
above the proportionality limit of the stress-strain curves. Moreover, the initial and post yielding stiffness weresimilar for the cyclic and monotonic loading cases, despite the 200 inelastic strain cycles. Interestingly, it was
found that the maximum deformation capacity of cyclically loaded specimen was about twice as large as themonotonic one for the 12.7-mm BL anchorage.
3.2 Ultimate deformation capacity
The ultimate stress and strain of specimens subjected to monotonic loading are shown in Fig. 6. The ultimateউঞ५ॺঞ५ॺ॥থॡজ‫৾ੵॺش‬ভ‫ؙ‬ਸ਼їћ৚३থএ४क़঒૛ધૐ‫ق‬їѕіќফіѕা‫ك‬〔論文〕

stress was estimated from the breaking load and nominal section, while the ultimate strain was taken from of H2curve. According to the results, all samples had an ultimate stress larger than 0.95fpu, complying with AIJ [6]. In
addition, CP anchors were able to maintain slightly higher ultimate stress than BL anchors. The ultimate
deformation capacity for all samples was limited by the fracture of few outer wires inside the anchorage zone;
therefore, full capacity of strands was not developed. Moreover, some samples of BL anchorages showed ultimate
strains less than 2%, while all CP samples had ultimate strains larger than 4%. As for the influence of strand
diameter, 12.7-mm strands showed larger, about two times in average, ultimate strain than 15.2-mm strands.

Ultimate stress (fp/fpu)

1.08

Table 2 Loading cases.

fpu, D15=1882 MPa
fpu, D12=1854 MPa

1.06
1.04

Code1.02
1.00

D15-BL-2-M

0.98

D12-BL-2-M

D15-CP-3-M

0.96

D12-CP-2-M

0.94

1234

Ultimate strain (%)

56ML1L2L3L4L5L6F min /F pu

F max /F pu

Frequency
(Hz)

0.40
0.50
0.40
0.50
0.30
0.50

0.95
0.90
0.95
0.90
0.95
0.95

331
134Fig. 6 Stress-strain curves under monotonic load
Figure 7 shows the influence of loading frequency and amplitude on the ultimate capacity for specimens
subjected to cyclic loading. CP anchorages reported about 1.8 times larger average ultimate strain capacity thanBL anchorages for 15.2-mm specimens. It was also observed that some specimens of 15.2-mm BL anchorages had
an ultimate strain capacity smaller than 2%. As for the 12.7-mm specimens, the CP anchorages also showed larger
ultimate strain capacity than BL anchorages; however unlike 15.2-mm strand specimens, all 12.7-mm specimens
had ultimate strain capacities over 2% and ultimate stresses over 1.0fpu. In addition, it was noted that 15.2-mmspecimens subjected to 1Hz loading reported the lowest deformation capacity (about 1.42%). Conversely, thefrequency showed no significant influence on the ultimate strain capacity of CP anchorage for neither 12.7-mm
nor 15.2-mm specimens. It is worth to mention that the ultimate strain capacity of BL anchorages showed larger
scatter than CP anchorages, which should be taken into account during the seismic design.
As it was mentioned before, three types of cyclic loading amplitudes were applied to the specimens: A1 from0.50 to 0.90fpu, A2 from 0.40 to 0.95fpu, and A3 from 0.30 to 0.95fpu. It was observed that the lowest deformationcapacity was produced during the smallest amplitude A1, whereas A3 reported the largest deformation capacity(3.86%) for 15.2-mm BL anchorages. As for 15.2-mm CP anchorages, the amplitude A3 actually reported thelowest deformation capacity of about 3.65%. Unlike 15.2-mm specimens, 12.7-mm samples subjected toamplitudes A1 and A2 did not show noticeable differences on deformation capacity. Even though A2 showedslightly larger ultimate strain values, no significant influence of loading amplitude was observed in 12.7-mm CP
anchorages.
3.3 Wedge seatingFigure 8 shows the typical relationship between tensile load and wedge seating ('t at the top and 'b at thebottom). The wedge seating under monotonic loads showed three stages: 1) rapid increase at low tensile load
levels, 2) slower increase of movement as load increases, 3) slightly more rapid movements followed by fracture.
In addition, BL anchorages showed smaller wedge seating at the ultimate stress than CP anchorages and 15.2-mm
specimens showed larger wedge seating than 12.7-mm ones. The specimen subjected to cyclic loading sustained
lower values of wedge seating than the monotonic loaded specimen; however, not clear influence of loadingparameters on the wedge seating was found. Furthermore, once the desired amplitude of loading was reached, thewedges kept the same displacement until additional load was applied as can be seen in the horizontal lines in Fig.
8. After the cyclic loading was finished, small wedge seating was observed above the yielding load. It was alsoobserved that 12.7-m specimens had smaller wedge seating at ultimate load than 15.2-mm specimens. In addition,
the maximum wedge seating was about 7.5mm (0.71% of Lps) for BL anchorage and 8.9mm (0.84% of Lps) for CP
anchorage. Although the influence of wedge seating was significant in the samples of this test, because a relatively
short length (about 1m) was used, the wedge seating may be less significant in practical application with larger
total strand lengths.

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instance, the average number of fractured wires at failure was 1.4 and 3.7 for BL and CP anchorage, respectively.
The relative movement of wedges inside anchorages induced localized stress concentration in outer wires ofstrands; moreover, since only the narrow part of wedges got in contact with the strands, no all the outer weregripped at the same time. This type of failure was observed in all the specimens with BL anchor, in whose cases,
only one or few wire fractured first.
4. CONCLUSIONS
Based on the test results, the following conclusions can be drawn. All the samples showed ultimate stresslarger than 0.95fpu, which complies with current standard requirements. The failure of the specimens occurred as apremature fracture of one or few strand wires inside the anchorages and two types of fractures were recognized:
the diagonal cut of the section and a sort of necking of some outer wires. The former fracture type was mainly
seen in BL anchorages, while the latter was mainly seen in CP anchorages. In addition, it was observed that nosample failed during the cyclic loading part of the protocol.
In general, CP anchors showed better ultimate strain capacity than BL anchors under the different loadingcases. For monotonic loaded specimens, the ultimate strain capacity was found to be between 4.45-4.70% in CP
and 1.51-3.99% in BL anchorages. As for the cyclic loaded specimens, the ultimate strain capacity ranged between
1.42 to 4.78% and 3.65 to 5.56% for BL and CP anchorage, respectively. The ultimate strain capacity of thesamples was by far smaller than fracture strain of 6% to 7% commonly reported in mill sheets of monostrand.
Moreover, deformation capacity of BL anchorage showed larger scatter than the one of CP.
Influence of loading frequency and amplitude was only found on the ultimate strain capacity of BLanchorages. In general, the influence of loading frequency and amplitude on the ultimate strain capacity wassmaller in 12.7-mm specimens than in 15.2-mm ones. The maximum wedge seating was about 7.5mm (0.71% ofLps) for BL anchorage and 8.9mm (0.84% of Lps) for CP anchorage.
The conclusions drawn in this study provide a significant insight on the behavior of unbonded anchorages;
however, they are valid only for the type of systems and for the loading conditions specified here. Therefore,
further research is needed to explore the response of different anchorage systems and with different loading
conditions.
ACKNOWLEDGMENTS
Financial support of the Peruvian National Council of Science, Technology, and Technological Innovation(CONCYTEC/CIENCIACTIVA) for the doctoral studies of the first author is acknowledged. Thanks to Sumitomo Steel
Wire Corp. (SEI-SSW) for its generous contribution to this research by donating strand and anchorages. The authors
recognize the kind support of Mr. Masato Yamada from SEI-SSW during the course of this research. All opinions,findings, and conclusions stated here are those of the authors and do not necessarily reflect the views of the supportinginstitutions.

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